Spanwise structuring and rivulet formation in suspended falling liquid films

Abstract

In suspended falling films, i.e., films on the underside of a bounding wall with arbitrary inclination, the surface film topology evolves towards a distinct spanwise structuring of the flow into rivulets, which is potentially accompanied by dripping events. Experimental data suggest a connection between long-term spanwise structuring and primary instabilities of the film surface. However, available experimental data regarding this connection remain nonconclusive. Hence, the present study aims at elucidating the evolution of a suspended falling film from varying imposed initial conditions to the emergence of spanwise modulations and rivulet formation. The study is carried out by means of extended numerical simulations employing a weighted residual integral boundary layer model for falling liquid films. The investigated parameter space covers recent experimental data on the topic. Varying imposed initial conditions, Reynolds number, Kapitza number, as well as wall inclination, several possible causes for a deviation of observed spanwise wavelengths from the one predicted by the primary Rayleigh-Taylor mechanism, are identified. This includes a distinct influence of initial conditions, asynchronous destabilization of consecutive wavefronts, competing short wave capillary instabilities, and rivulet interaction.